Graphical Models and Model Visualization

Comments

The different types of variables are represented by various icons. The following types are used:

binary variable	discrete (but not binary) variable	continuous variable

The significance of parameters could be displayed via linewidths.

These are variables u1 and u2 influencing the parameter assiciated to variable W. This occurs in varying coefficient models (see e.g. the work of Silke Edlich), where the parameters are not taken to be constant but smoothly varying over additional variables (in this case u1 and u2). This enables you to have (nonparametric) interactions.

For parametric interactions formally more boxes with two or more variables and a new parameter must be added. I think this is a severe weakness of this visualization approach. Maybe a variable lattice (similar to the interaction lattices of loglinear models) could be used.

Including varying coefficients requires additional parameters, in this case smoothing parameters. Since they are important for the model and should be accessible via the graphic, they are displayed. The linewidths could denote if the smoothing was locally (small lambda, high variation --> thick line) or globally (large lambda, almost constant parameter --> thin line).

The linear predictor eta is the first "result" of the model. It is a continuous variable, but the color is different, since this is a derived variable (as opposed to input variables such as u1 or x1). The reason that eta occurs in this picture at all is that it might be useful to have access to eta (for instance for plotting eta versus g(y) (g the link function) or versus residuals or versus an additional variable x).

The link function. I haven't found a satisfying way to display the link function besides giving a formula expression in the box.

This box annotates that the expectation of y is modeled, not y itself.

This dashed line denotes the dependency of mean and variance. For normal distributions mean and variance are independend, for gamma distributions they are not. Here I have the same problem as with the link function - no good way to show the kind of dependency.

Interactive features

Furthermore a lot of interactive features could be added. To name just a few:

• Interrogation. Almost everything could be interrogated, variables give (graphical or textual) summaries, parameters give parameter values and significances, etc. (Here is an example for graphical interrogation in loglinear graphical models)
• New variables can be added via drag and drop. Removal of variables as well.
• Clicking the connection between mean and variance could give a plot of mean(various subsamples) vs. variance(the same subsamples).
• User-accessible parameters like the smoothing parameters for varying coefficients could be changed via sliders or other graphical controls.